arXiv subjects
Publications and source records attributed to Kisan Bhoi.
Padovan sequence is a ternary recurrent sequence defined by the recurrence relation $P_{n+3}=P_{n+1}+P_{n}$ with initial terms $P_{0}=P_{1}=P_{2}=1.$ In this study it is shown that $114,151,200,265,351,465,616,816,3329,4410,7739,922111$ are the only Padovan numbers which are concatenations of three repdigits.
In this study we find all solutions of the Diophantine equation $B_{n_{1}}+B_{n_{2}}=2^{a_{1}}+2^{a_{2}}+2^{a_{3}}$ in positive integer variables $(n_{1},n_{2},a_{1},a_{2},a_{3}),$ where $B_{n}$ denotes the $n$-th balancing number.
In this study, we find all Pell and Pell-Lucas numbers which are sums of three base 10 repdigits. The proof of our main theorem uses lower bounds for linear forms in logarithms of algebraic numbers and a version of the Baker-Davenport reduction method.